GATE XE kind:question PYQs & Answers — Page 92

Questions 911–920 of 1772. Imported answers require independent review unless marked reviewed.

Topic practice 1772 questionsPage 92 of 178

Let

be a non-negative continuous function of real variable

. If the area under the curve

from

, then the value of

is ______ (round off to one decimal place).

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If the numerical approximation of the value of the integral

using the Trapezoidal rule with two subintervals is 9, then the value of the real constant

is ______ (round off to one decimal place).

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Let the transformation

reduce the ordinary differential equation

where

are real constants. Then, the arithmetic mean of

is ______ (round off to three decimal places).

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A person, who speaks the truth 3 out of 4 times, throws a fair dice with six faces and informs that the outcome is 5. The probability that the outcome is really 5 is ________ (round off to three decimal places).

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Let

be a real valued function. Then, which one of the following statements is TRUE for all

Your answerChoose one option.

is not a stationary point of

has a local maxima at

has a local minima at

has a saddle point at

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Let

be such that both

and

satisfy the Laplace equation in a domain

of the

-plane. Then, which one of the following is TRUE in

Your answerChoose one option.

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Let

denote the identity matrix of order 7, and

be a

real matrix having characteristic polynomial

, where

and

are positive integers. If

is diagonalizable and

, then

is ______ (in integer).

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Let

be the line segment from

, and let

be the arc of the circle

from

. If

where

, then the value of

is ________ (round off to two decimal places).

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The general relationship between shear stress,

, and the velocity gradient

for a fluid is given by

, where

is a constant with appropriate units. The fluid is Newtonian if

Your answerChoose one option.

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Which one of the following options is TRUE?

Your answerChoose one option.

Pathlines and streaklines are the same in an unsteady flow, and streamlines are tangent to the local fluid velocity at a point.

Streamlines are perpendicular to the local fluid velocity at a point, and streamlines and streaklines are the same in a steady flow.

Pathlines and streaklines are the same in an unsteady flow, and streamlines and streaklines are the same in a steady flow.

Streamlines are tangential to the local fluid velocity at a point, and streamlines and streaklines are the same in a steady flow.

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GATE XE kind:question PYQs

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